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Planar Spiral PCB Inductor Sizing Calculator

Planar spiral inductors printed directly on PCB copper layers eliminate discrete surface-mount components in RF filters, NFC antennas, and inductive sensors.

Maximum outside dimension of spiral inductor.

Width of spiral copper conductor trace.

Clearance spacing between adjacent spiral turns.

Total count of concentric winding turns (can be fractional).

Geometric layout shape of the printed planar coil.

Calculated Result
304.7 nH

Planar PCB Inductance

Nominal Inductance (L)

304.7 nH

Self-Resonant Freq (SRF)

~372 MHz

Inner Diameter (D_in)

6.6 mm

Average Diameter (D_avg)

9.3 mm

Fill Factor (ρ)

0.29

Geometry

SQUARE Spiral PCB Trace

Calculation Breakdown

  1. Spiral Dimensioning & Fill FactorD_in = 12 - 2 × 4.5 × (0.35 + 0.25) = 6.6 mm → ρ = (D_out - D_in) / (D_out + D_in) = 0.29
  2. Modified Wheeler / Mohan ApproximationL = [μ₀ × N² × D_avg × c₁ / 2] × [ln(c₂ / ρ) + c₃ρ + c₄ρ²] = 304.7 nH

Spiral Inductor Geometry & Metrics

Interactive visualization based on your current inputs

Value
0.03876114152Inductance (nH)SRF (MHz × 0.1)D_in (mm)D_avg (mm)ParameterValue

What Is the Planar Spiral PCB Inductor Sizing Calculator?

The Planar Spiral PCB Inductor Sizing Calculator designs printed copper coils directly on circuit boards for RF and wireless communications.

How Does the Planar Spiral PCB Inductor Sizing Calculator Work?

It computes coil geometric dimensions and solves closed-form modified Wheeler expressions derived from electromagnetic field theory.

Planar Spiral PCB Inductor Sizing Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

L = \frac{\mu_0 N^2 D_{avg} c_1}{2} \left[ \ln\left(\frac{c_2}{\rho}\right) + c_3 \rho + c_4 \rho^2 \right]

Mohan & Lee modified Wheeler planar electromagnetic formulation for spiral coils.

How to Use the Planar Spiral PCB Inductor Sizing Calculator

  1. Enter coil outer diameter in mm.
  2. Specify trace width and clearance spacing.
  3. Enter number of turns and select coil shape geometry.

Step-by-Step Example Calculation

4.5-Turn Square RF Spiral Inductor

Input Values:

outerDiameterMm:12
traceWidthMm:0.35
traceSpacingMm:0.25
numberOfTurns:4.5
shapeGeometry:square
Worked Steps: Yields 6.60 mm inner diameter, 0.290 fill factor, 151.7 nH nominal inductance, and ~170 MHz self-resonant frequency.

Understanding Your Result

Nominal Inductance: Self-inductance in nanohenries (nH).

Inner Diameter: Center clearance remaining inside the coil.

Self-Resonant Frequency: Upper operational frequency threshold before capacitive self-resonance.

Factors That Affect the Result

  • Inductance scales with the square of turns (N²): doubling turns roughly quadruples inductance.

When Should You Use This Calculator?

  • NFC / RFID tag antennas, RF front-end impedance matching networks, inductive proximity sensors, and DC-DC power converter modules.

Assumptions & Limitations

  • Assumes thin planar copper traces on low-loss RF or FR-4 dielectric substrates.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Based on IEEE MTT Mohan et al. Simple Accurate Expressions for Planar Spiral Inductances.

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